Autothrottle changes from EPR/N1 to SPD at the same time as ALT CAP occurs. Speed window opens at the actual IAS that was being flown when ALT CAP occurred. This is assuming you were climbing in VNAV rather than FLCH.
The autopilot pitches to achieve a smooth level off depending on rate of climb, the autothrottle provides thrust to fly the commanded speed. If you're slow, just increase the commanded speed.
The only time I've ever seen the speed low was in wave activity.